Network reliability‐based optimal toll design

Optimal toll design from a network reliability point of view is addressed in this paper. Improving network reliability is proposed as a policy objective of road pricing. A reliability‐based optimal toll design model, where on the upper level network performance including travel time reliability is optimized, while on the lower level a dynamic user‐equilibrium is achieved, is presented. Road authorities aim to optimize network travel time reliability by setting tolls in a network design problem. Travelers are influenced by these tolls and make route and trip decisions by considering travel times and tolls. Network performance reliability is analyzed for a degradable network with elastic and fluctuated travel demand, which integrates reliability and uncertainty, dynamic network equilibrium models, and Monte Carlo methods. The proposed model is applied to a small hypothesized network for which optimal tolls are derived. The network travel time reliability is indeed improved after implementing optimal tolling system. Trips may have a somewhat higher, but more reliable, travel time.     

Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand

Network pricing serves as an instrument for congestion management, however, agencies and planners often encounter problems of estimating appropriate toll prices. Tolls are commonly estimated for a single-point deterministic travel demand, which may lead to imperfect policy decisions due to inherent uncertainties in future travel demand. Previous research has addressed the issue of demand uncertainty in the pricing context, but the elastic nature of demand along with its uncertainty has not been explicitly considered. Similarly, interactions between elasticity and uncertainty of demand have not been characterized. This study addresses these gaps and proposes a framework to estimate nearest optimal first-best tolls under long-term stochasticity in elastic demand. We show first that the optimal tolls under the deterministic-elastic and stochastic-elastic demand cases coincide when cost and demand functions are linear, and the set of equilibrium paths is constant. These assumptions are restrictive, so three larger networks are considered numerically, and the subsequent pricing decisions are assessed. The results of the numerical experiments suggest that in many cases, optimal pricing decisions under the combined stochastic-elastic demand scenario resemble those when demand is known exactly. The applications in this study thus suggest that inclusion of demand elasticity offsets the need of considering future demand uncertainties for first-best congestion pricing frameworks.     

Congestion pricing under operational,supply-side uncertainty

This paper is concerned with finding first-best tolls in static transportation networks with day-to-day variation in network capacity, as accounted for by changes in the volume-delay function. The key question in addressing this problem is that of information, namely, which agents have access to what information when making decisions. In this work, travelers are assumed to be either fully informed about network conditions before embarking on travel, or having no information except the probability distributions; likewise, the network manager (toll-setter) is either able to vary tolls in response to realized network conditions, or must apply the same tolls every day. Further, travelers’ preference for reliable travel is accounted for, representing risk aversion in the face of uncertainty. For each of the scenarios implied by combinations of these assumptions, we present methods to determine system-optimal link prices. A demonstration is provided, using the Sioux Falls test network, suggesting that attempts to incorporate uncertainty into nonresponsive tolls involve significantly higher prices.     

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem

This paper is concerned with roadway pricing amidst the uncertainty which characterizes long-term transportation planning. Uncertainty is considered both on the supply-side (e.g., the effect of incidents on habitual route choice behavior) and on the demand-side (e.g., due to prediction errors in demand forecasting). The framework developed in this paper also allows the benefits of real-time travel information to be compared directly against the benefits of responsive pricing, allowing planning agencies to identify the value of these policy options or contract terms in publicly-operated toll roads. Specifically, six scenarios reflect different combinations of policy options, and correspond to different solution methods for optimal tolls. Demonstrations are provided on both the Sioux falls and Anaheim networks. Results indicate that providing information to drivers implemented alongside responsive tolling may reduce expected total system travel time by over 9%, though more than 8% of the improvement is due to providing information, with the remaining 1% improvement gained from responsive tolling.     

Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts

Trucking companies (carriers) are increasingly facing combinatorial auctions conducted by shippers seeking contracts for their transportation needs. The bid valuation and construction problem for carriers facing these combinatorial auctions is very difficult and involves the computation of a number of NP-hard sub problems. In this paper we examine computationally tractable approximation methods for estimating these values and constructing bids. The benefit of our approximation method is that it provides a way for carriers to discover their true costs and construct optimal or near optimal bids by solving a single NP-hard problem. This represents a significant improvement in computational efficiency. We examine our method both analytically and empirically using a simulation based analysis.     

Integrating congestion pricing,transit subsidies and mode choice

We model and analyze optimal (welfare maximizing) prices and design of transport services in a bimodal context. Car congestion and transit design are simultaneously introduced and consumers choose based on the full price they perceive. The optimization variables are the congestion toll, the transit fare (and hence the level of subsidies) and transit frequency. We obtain six main results: (i) the optimal car-transit split is generally different from the total cost minimizing one; (ii) optimal congestion and transit price are interdependent and have an optimal frequency attached; (iii) the optimal money price difference together with the optimal frequency yield the optimal modal split; (iv) if this modal split is used in traditional stand-alone formulations – where each mode is priced independently–resulting congestion tolls and transit subsidies and fares are consistent with the optimal money price difference; (v) self-financing of the transport sector is feasible; and (vi) investment in car infrastructure induces an increase in generalized cost for all public transport users.     

Dynamic pricing for managed lanes with multiple entrances and exits

Priced managed lanes are increasingly being used to better utilize the existing capacity of the roadway to relieve congestion and offer reliable travel time to road users. In this paper, we investigate the optimization problem for pricing managed lanes with multiple entrances and exits which seeks to maximize the revenue and minimize the total system travel time (TSTT) over a finite horizon. We propose a lane choice model where travelers make online decisions at each diverge point considering all routes on a managed lane network. We formulate the problem as a deterministic Markov decision process and solve it using the value function approximation (VFA) method for different initializations. We compare the performance of the toll policies predicted by the VFA method against the myopic revenue policy which maximizes the revenue only at the current timestep and two heuristic policies based on the measured densities on the managed and general purpose lanes (GPLs). We test the results on four different test networks. The primary findings from our research suggest the usefulness of the VFA method for determining dynamic tolls. The best-found objective value from the method at its termination is better than other heuristics for all test networks with average improvements in the objective ranging between 10% and 90% for revenue maximization and 0–27% for TSTT minimization. Certain VFA initializations obtain best-found toll profiles within first 5–50 iterations which warrants computational time savings. Our findings also indicate that the revenue-maximizing optimal policies follow the “jam-and-harvest” behavior where the GPLs are pushed towards congestion in the earlier time steps to generate higher revenue in the later time steps, a characteristic not observed for the policies minimizing TSTT.     

Estimating commuter mode choice: A discrete choice analysis of the impact of road pricing and parking charges

Automobile use leads to external costs associated with emissions, congestion, noise and other impacts. One option for minimizing these costs is to introduce road pricing and parking charges to reduce demand for single occupant vehicle (SOV) use, while providing improvements to alternatives to encourage mode switching. However, the impact of these policies on urban mode choice is uncertain, and results reported from regions where charging has been introduced may not be transferable. In particular, revealed preference data associated with cost recovery tolls on single facilities may not provide a clear picture of driver response to tolls for demand management. To estimate commuter mode choice behaviour in response to such policies, 548 commuters from a Greater Vancouver suburb who presently drive alone to work completed an individually customized discrete choice experiment (DCE) in which they chose between driving alone, carpooling or taking a hypothetical express bus service when choices varied in terms of time and cost attributes. Attribute coefficients identified with the DCE were used in a predictive model to estimate commuter response to various policy oriented combinations of charges and incentives. Model results suggest that increases in drive alone costs will bring about greater reductions in SOV demand than increases in SOV travel time or improvements in the times and costs of alternatives beyond a base level of service. The methods described here provide an effective and efficient way for policy makers to develop an initial assessment of driver reactions to the introduction of pricing policies in their particular regions.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

Accounting for travel time variability in the optimal pricing of cars and buses

A number of studies have shown that in addition to travel time and cost as the common influences on mode, route and departure time choices, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean–variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars, buses and walking as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.     

Global convergence of the trial-and-error method for the traffic-restraint congestion-pricing scheme with day-to-day flow dynamics

The traffic-restraint congestion-pricing scheme (TRCPS) aims to maintain traffic flow within a desirable threshold for some target links by levying the appropriate link tolls. In this study, we propose a trial-and-error method using observed link flows to implement the TRCPS with the day-to-day flow dynamics. Without resorting to the origin–destination (O–D) demand functions, link travel time functions and value of time (VOT), the proposed trial-and-error method works as follows: tolls for the traffic-restraint links are first implemented each time (trial) and they are subsequently updated using observed link flows in a disequilibrium state at any arbitrary time interval. The trial-and-error method has the practical significance because it is necessary only to observe traffic flows on those tolled links and it does not require to wait for the network flow pattern achieving the user equilibrium (UE) state. The global convergence of the trial-and-error method is rigorously demonstrated under mild conditions. We theoretically show the viability of the proposed trial-and-error method, and numerical experiments are conducted to evaluate its performance. The result of this study, without doubt, enhances the confidence of practitioners to adopt this method.     

Can Hong Kong price-manage its cross-harbor-tunnel congestion?

Hong Kong drivers face daily congestion, especially at the Cross Harbor Tunnel (CHT) whose tolls are substantially lower than those of the drivers’ other two tunnel options: the Eastern Harbor Crossing (EHC) and the Western Harbor Crossing (WHC). In 2013, the Hong Kong Special Administrative Region (HKSAR) Government issued a consultation paper, seeking public comments on three toll-change proposals that would raise the CHT’s tolls and lower the EHC’s tolls. The WHC’s tolls would remain unchanged due to its congested connecting roads. Using monthly crossing data available from the HKSAR’s Transport Department for 2000–2012, this paper uses a Generalized Leontief demand system to document that the usage patterns of the three tunnels is price-responsive. Hence, we conclude that the proposed toll changes are likely to be effective in transportation demand management, by shifting a portion of the CHT’s usage to the EHC and WHC, thereby relieving the CHT’s congestion.     

Activity-based disaggregate travel demand model system with activity schedules

We present an integrated activity-based discrete choice model system of an individual’s activity and travel schedule, for forecasting urban passenger travel demand. A prototype demonstrates the system concept using a 1991 Boston travel survey and transportation system level of service data. The model system represents a person’s choice of activities and associated travel as an activity pattern overarching a set of tours. A tour is defined as the travel from home to one or more activity locations and back home again. The activity pattern consists of important decisions that provide overall structure for the day’s activities and travel. In the prototype the activity pattern includes (a) the primary – most important – activity of the day, with one alternative being to remain at home for all the day’s activities; (b) the type of tour for the primary activity, including the number, purpose and sequence of activity stops; and (c) the number and purpose of secondary – additional – tours. Tour models include the choice of time of day, destination and mode of travel, and are conditioned by the choice of activity pattern. The choice of activity pattern is influenced by the expected maximum utility derived from the available tour alternatives.     

A multi-criteria evaluation of solutions and alternatives for matching capacity to demand in an airport system: the case of London

This paper applies multi-criteria decision-making (MCDM) methods to the evaluation of solutions and alternatives for matching airport system airside (runway) capacity to demand. For such a purpose, ‘building a new runway’ is considered as the solution and candidate airports of the system as alternatives for implementing the solution. The alternative airports are characterized by their physical/spatial, operational, economic, environmental, and social performance represented by corresponding indicator systems which, after being defined and estimated under given operating scenarios, are used as evaluation attributes/criteria by the selected MCDM methods. Two MCDM methods – Simple Additive Weighting and Technique for Order of Preference by Similarity to Ideal Solution – are applied to the case of the London airport system to rank and select the preferred alternative from three candidate airports – Heathrow, Gatwick, and Stansted – for where a new runway could be built.     

Design of public transit network in urban area with elastic demand

This research focuses on an efficient design of transit network in urban areas. The system developed is used to create, analyze and optimize routes and frequencies of transit system in the network level. The analysis is based on elastic demand, so the shift of demand between modes in network due to different service level is of prime consideration. The developed system creates all feasible routes connecting all pairs of terminals in the network. Out of this vast pool of routes, a set of optimal routes is generated for a certain predetermined number that maintains connectivity of significant demand. Based on these generated routes, the system fulfils transportation demand by assigning demand that considers path and route choices for non-transit users and transit users. Together with the assignment of demand, transit frequencies are optimized and the related fleet-size is calculated. Having an optimal setting of solution, the system is continued by reconnecting the routes to find some other better solutions in the periphery of the optimal setting. A set of mathematical programming modules is developed. Real data from Sioux Falls city network is used to evaluate the performance of the model and compare with other heuristic methods.     

Urban highway congestion

This article examines urban highway congestion pricing in the instance in which it is not possible to levy a congestion toll on a major portion of the urban road system. This case is pertinent because of technical and/or political constraints. The article uses economic theory and numerical examples to show that the optimum second-best toll can vary appreciably from the optimal tolls in a regime in which efficient tolls can be imposed on all routes.     

Design of income-equitable toll prices for high occupancy toll lanes in a single toll facility

Income inequity potentially exists under high occupancy toll (HOT) lanes whereby higher-income travelers may reap the benefits of the facility. An income-based multi-toll pricing approach is proposed for a single HOT lane facility in a network to maximize simultaneously the toll revenue and address the income equity concern, while ensuring a minimum level-of-service on the HOT lanes and that the toll prices do not exceed pre-specified thresholds. The problem is modeled as a bi-level optimization formulation. The upper level model maximizes revenue for the tolling authority subject to pre-specified upper bounds on tolls. The lower level model solves the stochastic user equilibrium problem. An agent-based solution approach is used to determine the toll prices by considering the tolling authority and commuters as agents. Results from numerical experiments indicate that a multi-toll pricing scheme is more equitable and can yield higher revenues compared to a single toll price scheme across travelers.     

Optimal dynamic parking pricing for morning commute considering expected cruising time

This paper investigates how recurrent parking demand can be managed by dynamic parking pricing and information provision in the morning commute. Travelers are aware of time-varying pricing information and time-varying expected occupancy, through either their day-to-day experience or online information provision, to make their recurrent parking choices. We first formulate the parking choices under the User Equilibrium (UE) conditions using the Variational Inequality (VI) approach. More importantly, the System Optimal (SO) parking flow pattern and SO parking prices are also derived and solved efficiently using Linear Programming. Under SO, any two parking clusters cannot be used at the same time by travelers between more than one Origin–Destination (O–D) pairs. The SO parking flow pattern is not unique, which offers sufficient flexibility for operators to achieve different management objectives while keeping the flow pattern optimal. We show that any optimal flow pattern can be achieved by charging parking prices in each area that only depend on the time or occupancy, regardless of origins and destinations of users of this area. In the two numerical experiments, the best system performance is usually achieved by pricing the more preferred (convenient) area such that it is used up to a terminal occupancy of around 85–95%. Optimal pricing essentially balances the parking congestion (namely cruising time) and the level of convenience.     

System optimum and pricing for the day-long commute with distributed demand,autos and transit

The day-long system optimum (SO) commute for an urban area served by auto and transit is modeled as an auto bottleneck with a capacitated transit bypass. A public agency manages the system’s capacities optimally. Commuters are identical except for the times at which they wish to complete their morning trips and start their evening trips, which are given by an arbitrary joint distribution. They value unpunctuality – their lateness or earliness relative to their wish times – with a common penalty function. They must use the same mode for both trips. Commuters are assigned personalized mode and travel start times that collectively minimize society’s generalized cost for the whole day. This includes unpunctuality penalties, queuing delays, travel times and out-of-pocket costs for users, as well as travel supply costs and externalities for society.It is shown that in a SO solution there can be no queuing and that the set of SO solutions forms a convex set. Furthermore, if the schedule penalty that users suffer due to unpunctuality is separable into morning and evening components, then the set of commuters traveling by the same mode arrive at work and depart from work in the order of their wishes. These orders are in general different in the morning and the evening. It is also shown that there always is a SO solution in which users are at all times, and on both modes, either punctual or flowing at capacity. These problem properties are used to identify search methods, both, for SO solutions and for time-dependent tolls and transit fares that preserve the solutions as Nash equilibriums. In every case studied, these prices exist. They must peak concurrently for the two modes in both periods.In special cases involving only one mode, only one period or concentrated demand the solution to the complete problem decomposes by period conditional on the number of transit users, and this facilitates the solution. In these cases the day-long SO cost is the sum of the SO costs for the two peaks considered separately. However, this is not true in general – the solution obtained by combining the two single-period solutions can be infeasible. When this happens, the optimum day-long cost will exceed the sum of the single-period costs. The discrepancy is about 40% of the total schedule penalty for an example representing a large city. Thus, to develop realistic policies the day-long problem must be addressed head on. An approximate method that yields closed form formulas for the case with uniformly distributed wishes is presented.